M3D Hessian_rot = Jacobian_rot.transpose() * Jacobian_rot;

Jacobian_rot is a mutable matrix with 3 columns. Add more data to Jacobian_rot.

1. Positive Semi-Definiteness: Since Hessian_rot is derived from a product of Jacobian_rot, it is positive semi-definite. Adding more rows cannot reduce the eigenvalues of Hessian_rot; it can only increase them or keep them the same.
2. Eigenvalue Magnitudes:
   • If the new rows of Jacobian_rot introduce significant variation or directions that were not well-represented before, the largest eigenvalue of Hessian_rot will likely increase.
   • The smallest eigenvalue (if positive) might also increase if the new rows provide more coverage in directions that were previously underrepresented.
   • If the new rows are linearly dependent on existing rows, the eigenvalues may not change significantly.

skew-symmetric matrix(antisymmetric matrix)

𝐴𝑇=−𝐴

1. Diagonal entries are all zero.
2. Eigenvalues are purely imaginary or zero.
3. Dimension of space of skew-symmetric